The hypothesis that sleep participates in the consolidation of recent memory traces has been investigated using four main paradigms: (1) effects of post-training sleep deprivation on memory consolidation, (2) effects of learning on post-training sleep, (3) effects of within sleep stimulation on the sleep pattern and on overnight memories, and (4) re-expression of behavior-specific neural patterns during post-training sleep. These studies convincingly support the idea that sleep is deeply involved in memory functions in humans and animals. However, the available data still remain too scarce to confirm or reject unequivocally the recently upheld hypothesis that consolidations of non-declarative and declarative memories are respectively dependent upon REM and NREM sleep processes.